Educational Studies in Mathematics

, Volume 97, Issue 1, pp 93–109 | Cite as

Inverse function: Pre-service teachers’ techniques and meanings

  • Teo PaolettiEmail author
  • Irma E. Stevens
  • Natalie L. F. Hobson
  • Kevin C. Moore
  • Kevin R. LaForest


Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss our inferences of their meanings based on their activities. We conclude with implications for the teaching and learning of inverse function and areas for future research.


Function Inverse function Pre-service secondary teachers Meanings 



This material is based upon work supported by the NSF under Grant No. DRL-1350342. Any opinions, findings, conclusions, or recommendations expressed are those of the authors. We thank Neil Hatfield for directing us to a notation for inverse function and Nick Wasserman for his feedback on an earlier draft.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Teo Paoletti
    • 1
    Email author
  • Irma E. Stevens
    • 2
  • Natalie L. F. Hobson
    • 3
  • Kevin C. Moore
    • 2
  • Kevin R. LaForest
    • 2
  1. 1.Mathematical Sciences DepartmentMontclair State UniversityMontclairUSA
  2. 2.Department of Mathematics and Science EducationUniversity of GeorgiaAthensUSA
  3. 3.Department of Mathematics and StatisticsSonoma State UniversityRohnert ParkUSA

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